The New Flat Earth Society

Albert A. Bartlett

This is a slightly revised version of an article that was published in the
September 1996 issue of The Physics Teacher, Vol. 34, No. 6, Pgs. 342-343.
This journal is published by the American Association of Physics Teachers,
College Park, MD.

INTRODUCTION: THE PROBLEM

There was a time, long ago, when people thought that the Earth was
flat,
but now for several centuries people have believed that the Earth is round
. . . like a sphere. But there are problems with a spherical earth, and a
now a new paradigm is emerging which seems to be a return to the wisdom of
the ancients.

A sphere is bounded and hence is finite, which implies that there
are
limits, and in particular, there are limits to growth of things that
consume the Earth and that live on it. Today, many people believe that the
resources of the Earth and of the human intellect are so enormous that
population growth can continue and that there is no danger that we will
ever run out of anything. For instance, after a United Nations report
predicted shortages of natural resources that would follow because of
continued population growth, Jack Kemp, who was then Secretary of Housing
and Urban Development in the Cabinet of President George Bush, is reported
to have said, "Nonsense, people are not a drain on the resources of the
planet." (2)

These people believe that perpetual growth is desireable,
consequently it
must be possible, and so it can't possibly be a problem. At the same time
there are still a few remaining "spherical earth" people who go around
talking about "limits" and in particular about the limits that are implied
by the term "carrying capacity." But limits are awkward, because limits
conflict with the concept of perpetual growth, so there is a growing move
to do away with the concept of limits. A friend recently returned from an
international conference in Germany and he reports that whenever he brought
up the subject of limits, the angry rebuttal was, "We're tired of hearing
of limits to growth! We're going to grow the limits!" Another friend
sent me a clipping (3) in which an eminent national economist closes an
opinion piece by saying:

A 3% to 3.5% growth rate is not only an achievable national objective: it
is an economic and social necessity.
A spherical earth is finite. The pro-growth people say that
perpetual
growth on this earth is possible. If the pro-growth people are correct,
what kind of an earth are we living on?

THE SOLUTION

A spherical earth is finite and hence is forever unappealing to the
devotees of perpetual growth. In contrast, a flat earth can accomodate
growth forever, because a flat earth can be infinite in the two horizontal
dimensions and also in the vertical downward direction. The infinite
horizontal dimensions forever remove any fear of crowding as population
grows, and the infinite downward dimension assures humans of an unlimited
supply of all of the mineral raw materials that will be needed by a human
population that continues to grow forever. The flat earth removes all the
need for worry about limits.

So, let us think of the "We're going to grow the limits!" people as
the
"New Flat Earth Society."

EXAMPLE

The economist Julian Simon is famous for his belief that there are
no
limits to growth. (4) In a recent article he wrote (5)

Technology exists now to produce in virtually inexhaustable
quantities
just about all the products made by nature - foodstuffs, oil, even pearls
and diamonds . . .

We have in our hands now - actually in our libraries - the
technology to
feed, clothe and supply energy to an ever-growing population for the next 7
billion years . . .

Even if no new knowledge were ever gained . . . we would be able to
go on
increasing our population forever . . . (6)

Two friends wrote me to call my attention to this article, and one
of them
said in his letter that Simon had been contacted and that Simon said that
the
"7 billion years" was an error and it should have been "7 million years."
(7)

We should note two things. First, there is a big difference between
"million" and "billion." In the U.S. a "billion" is a thousand million.
Second, even 7 million years is a long period of time.
One of these friends asked me: if the world population in 1995 is
5.7
billion people (5.7 x 109), what would its size be (P7) if it grew
steadily at 1% per year for 7 million years ? (8)

ARITHMETIC

Although arithmetic is falling out of fashion, let's do some
calculations
so that we can understand how the old fashioned "spherical earth"
scientists would treat the problem.

We will do this calculation assuming the length of time is exactly
7
million years and the growth rate is exactly 1% per year. For the case
of an annual growth rate of 1% , the value of k is 0.010 . . . per
year. It is easy enough to set up the equation for P7 , which is the
world population after 7 million years of 1% annual growth:

1) P7 = (5.7 x 109) exp(0.01 x 7 x l06)

= (5.7 x l09) exp(7 x 104)

Here is where we separate out those who understand algebra from those who
only know how to do key strokes on a calculator. When you do the
keystrokes to evaluate exp(7 x 104) many calculators will flash
the message "ERROR" because these calculators are not able to handle
numbers larger than 9.99... x 1099. (9) One must have some understanding
of algebra to work around this limitation.

What we want to find is the value of B in Eq.2.

2) exp(7 x 104) = 10B

If we take the natural logarithm of both sides we have

7 x 104 = B ln(10)

B = 7 x 104 / 2.303 . . .

3) B = 30400.6137 . . .

(Remember that we assumed the input numbers were exact.) Equation 1 now
becomes

P7 = 5.7 x 109 x 1030400.6137 . . .

4) = 5.7 x 1030409.6137 . . .

If one wants to express this as an integer power of ten, we can note that
100.6137 = 4.11, so that

P7 = 5.7 x 4.11 x 1030409

5) P7 = 2.3 x 1030410

This is a fairly large number!

If we had used Simon's original number of 7 billion years, we
would have
had B = 3.04 x 107.

It is hard to imagine the meaning of a number as large as the one
given in
Eq.5. To try to understand the meaning of this large number, let us
compare it with an estimate the number of atoms in the known universe. If
we assume the known universe is a sphere whose radius is 20 billion light
years, the volume of the sphere is about 3 x 1085 cubic centimeters. If
the average density of the universe is one atom per cubic centimeter, then
the number of atoms estimated to be in the known universe is about 3 x
1085. The number given in Eq.5 is something like 30 kilo-orders of
magnitude larger than the number of atoms estimated to be in the known
universe!

Note that in making this calculation we are assuming that the
universe,
like the Earth, is spherical, which could hardly be correct if the Earth is
flat and is of infinite lateral extent.

A related question comes to mind: if world population growth
continues at
a rate of 1% per year, (k = 0.01 per year) how long would it take for
the population to grow until the number of people was equal to this
estimate of the number of atoms in the known universe? This calls for us
to find t in the following equation.

6) 3 x 1085 = 5.7 x 109 exp(0.01 t)

5.26 x 1075 = exp(0.01 t)

174 = .01 t

t = 17 thousand years

This indicates that the population of the Earth, growing at 1% per year,
would grow to a number equal to the number of atoms estimated to be in the
known universe, in a period of time something like the period since a
recent ice age.
We could also ask, what growth rate would be required for the world
population to grow from 5.7 x 109 to 3 x 1085 in 7 million years? We
must find the value of k in this equation

7) 3 x 1085 = 5.7 x 109 exp(7 x 106 k)

Solving this, we find k = 2.5 x 10-5 per year. This is 2.5 x 10-3
percent per year. In the first year this growth rate would produce an
increase of world population of about 1.42 x 105 people. Contrast this
with the present increase of about 9 x 107 per year.

These numbers make it clear to us old fashioned "spherical earth
people"
that the world population cannot continue to grow for long at anything like
its present rate. There are signs that the population growth rate is
already slowing in some parts of Europe and Asia.

Calculations similar to these remind us that the major effect of
steady
growth in the rates of consumption of non-renewable resources is to shorten
dramatically the life-expectancy of the resources. (10)

Julian Simon has claimed that the human mind is "the ultimate
resource."
As was noted in the review of his 1981 book, this is true "only if it [the
human mind] is used." (11)

CONCLUSION

If the "we can grow forever" people are right, then they will expect
us,
as scientists, to modify our science in ways that will permit perpetual
growth. We will be called on to abandon the "spherical earth" concept and
figure out the science of the flat earth. We can see some of the problems
we will have to solve. We will be called on to explain the balance of
forces that make it possible for astronauts to circle endlessly in orbit
above a flat earth, and to explain why astronauts appear to be weightless.
We will have to figure out why we have time zones; where do the sun, moon
and stars go when they set in the west of an infinite flat earth, and
during the night, how do they get back to their starting point in the east.
We will have to figure out the nature of the gravitational lensing that
makes an infinite flat earth appear from space to be a small circular flat
disk. These and a host of other problems will face us as the "infinite
earth" people gain more and more acceptance, power and authority. We need
to identify these people as members of "The New Flat Earth Society"
because a flat earth is the only earth that has the potential to allow the
human population to grow forever.

(6) The Cato Institute report identifies the author: "Julian L. Simon
is
a professor of business and management at the University of
Maryland and
an adjunct scholar at the Cato Institute. This essay [from which these
quotations are taken] is based on the introduction to his latest book,
The State of Humanity, just published by the Cato Institute and Blackwell
Publishers."

The Cato Institute is a think tank in Washington, D.C. that
advises
government leaders on policy questions.

At the annual meeting in February of 1995, Julian Simon was
elected a
Fellow of the American Association for the Advancement of Science.

(7) I am indebted to Mark Nowak of Population, Environment,
Balance, in
Washington, D.C. and Dr. John Tanton, Petosky, MI, for calling this article
to my attention.

(8) The growth rate of world population in the early 1990s was around
1.7% per year.

(9) In doing these calculations, I was surprised to find that my new
Hewlett- Packard Model 20S hand-held calculator will handle powers of
ten
up to 500.